I prefer to mix my own clay bodies from refined raw clays (see below for recipes). This lets me make variations in recipes, dictate the stiffness or wetness of the clay prior to storage, and mix certain bodies that call for extra attention in special ways. The alternative to mixing your own clay is to buy it premixed from a supplier (which I also do on occasion, especially in the case of a porcelaneous or "white" stoneware body from Laguna or Amaco).
I generally try to make my clay several months in advance, and am really pleased when I can get as far as a year ahead - this lets it age and acquire all those great working properties that can't really be had any other way. (Legend has it that Japanese potters used the clay they inherited from their fathers, and made clay to pass down to their sons...) In recent years, I've used four different bodies:
I mix clay in one of two ways: by claymixer/dough mixer or by mixing a slip that air dries slowly in racks. A claymixer like this Soldner mixer is a great tool: it mixes a batch of clay fast, is relatively easy to clean (allowing for mixing different batch types in succession), and - obviously - does most of the hard work. Drawbacks are the initial investment and that a batch from new materials is short and hard to work with (without a good proportion of aged slops to start from). That won't stop me from buying my own one day - they are practically indispensible to making mixing large quantites of clay.
For smaller batches, drying out slops, or mixing bodies that need better initial workability, I mix the body recipe as a thick slip and then set it out to dry. I learned this mixing method from Clary Illian while working in her studio. I like its low-tech aspects: it's very direct and can be done with very little equipment. I use a 55 gallon trashcan, a 3/8" drill with large mixer attachment, and drying racks made of 2x4's, wire mesh, and old bedsheets. The water in the clay gradually soaks out through the sheets below and air dries from the top. For faster drying, I put the racks outside in the sun; for slower, inside or in the shade. This process works well with porcelain clays. They really benefit from a longer contact time with the water; it penetrates between the clay particles more, resulting in better plasticity.
I typically store clay a bit damper than I actually prefer to throw, which helps prevent it drying out if stored a long time and improves plasticity while waiting, so I have some plaster bats in the studio to dry it to the right consistency just before throwing. Some of the premixed clay I use comes pretty damp, so I use the same approach for that too.
Bagged clay, waiting in the studio. I like large lawn bags, because they allow for several wraps around each 40-50# chunk of clay, keeping the original moisture in for a long period of time. It's reassuring to me to have a thousand pounds of clay hanging around, just in case.
My two primary clay bodies are listed below. Both are for cone 10 firing and I've used both in gas reduction, salt/soda, and wood fired kilns with pretty good results. The ASU Red body is better in gas reduction, the Johnston stoneware is better in salt/soda and wood.